The Zariski problem for function fields of quadratic forms

Ohm, Jack

doi:10.1090/S0002-9939-96-03238-8

The Zariski problem for function fields of quadratic forms
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Proc. Amer. Math. Soc. 124 (1996), 1679-1685 Request permission

Abstract:

By ‘a quadratic function field’ is meant the affine function field of a nonsingular quadratic form of dimension $> 2$. What quadratic function fields contain a given quadratic function field $k(P)$? This problem is solved here for quadratic forms $P$ of dimensions 3 and 4, and an application to the Zariski cancellation problem for quadratic function fields is given.

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